Research Article Improved Mainlobe Interference ...downloads.hindawi.com/journals/jece/2015/964901.pdf · Research Article Improved Mainlobe Interference Suppression Based on Blocking

Research ArticleImproved Mainlobe Interference SuppressionBased on Blocking Matrix Preprocess

Jie Yang1 and Congfeng Liu2

1School of Communication and Information, Ai’an University of Post & Telecommunication, Xi’an, Shaanxi 710121, China2Research Institute of Electronic Countermeasure, Xidian University, Xi’an, Shaanxi 710071, China

Correspondence should be addressed to Congfeng Liu; [email protected]

Received 10 February 2015; Revised 19 March 2015; Accepted 20 March 2015

Academic Editor: John N. Sahalos

Copyright © 2015 J. Yang and C. Liu. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

For the problem of mainlobe direction shifting that is caused by the mainlobe interference suppression based on blocking matrixpreprocess, an effective method is proposed which is based on the combination of diagonal loading and linear constraints.Therein,the reason formainlobe direction shifting is analyzed and found to be that the covariancematrixmismatch exists in the realization ofthe adaptive beamforming.Therefore, the diagonal loading processing is used to overcome the mismatch and correct the mainlobedirection shifting, and the linear constraints are used to make sure of the beam pattern nulling in the interference directions; thenthe desired performance of adaptive beamforming is obtained. Simulation results attest the correctness and effectiveness of theproposed method, and they also show that the proposed method is insensitive to the selection of diagonal loading level, whichmeans the loading factor is easy to choose.

1. Introduction

The adaptive array can be used to suppress the spaceinterference effectively, especially when the interferences arelocated out of the mainlobe. Array antenna can realize theinterference suppression by efficient adaptive beamform-ing algorithm; however, when the interference is locatedin the mainlobe, the conventional adaptive beamformingtechniqueswill lead to the sidelobe level rising andmainbeamdirection shifting; then the desired signal will be not in thebeampointing direction, and the output signal to interferenceplus noise ratio (SINR) will decline and the false-alarmprobability will rise sharply;meanwhile themainlobe shiftingwill affect the accuracy of angle estimation [1–6]. When theadaptive beamformer suppresses the mainlobe interference,it must form the null in the interference direction which isinside the mainlobe.

At present, many methods are put forward to suppressthe mainlobe interference [5–9], but when the mainlobeinterference is eliminated, there will be some other problemsat the same time, such as the mainlobe direction shifting andsidelobe rising. Mainlobe interference suppression algorithmwhich is based on the blocking matrix preprocess attracted

extensive attention due to the clear ideas and remarkableeffect [6], but this method also leads to the problem ofthe mainlobe direction shifting. Therefore, this paper putsforward the new method depending on the combinationof diagonal loading and linear constraints to improve theperformance of the adaptive beamformer after the blockingmatrix preprocess. This paper not only analyses the reasonof the direction shifting of beamforming algorithm basedon the blocking matrix preprocess in theory, but also givesthe corresponding solution which is simple and effective inrealization.

2. Mainlobe Interference SuppressionBased on Blocking Matrix Preprocess

Assuming an interference is inside the mainlobe, in orderto suppress it, we should first estimate its location in themainlobe with the spatial spectrum estimation algorithm.Because the power of the interference is usually muchstronger than that of the signal and noise, the MUSIC orother algorithms can be used, such as ESPRIT andmaximumlikelihood estimator [10, 11].Thedirection of arrival (DOA) of

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2015, Article ID 964901, 8 pageshttp://dx.doi.org/10.1155/2015/964901

2 Journal of Electrical and Computer Engineering

the mainlobe interference can be estimated based onMUSICalgorithm; the formula is given as [11]

𝑃MUSIC =1

a𝐻 (𝜃)U𝑁U𝐻𝑁a (𝜃), (1)

where U𝑁

is the eigenvector matrix of the noise subspacebased on the eigendecomposition of the covariance matrixR of the received array data. a(𝜃) is the steering vector. TheDOAs which correspond to the MUSIC spectral peak are theestimated incident directions of the signal and interference.Since the DOA of mainlobe interference is only estimated,the angle searching range only needs to be constrained inthe mainlobe width, which can greatly reduce the amount ofcomputation.

When the DOA of the mainlobe interference is obtained,take the preprocess of the mainlobe interference cancellationto the received array signals X. Assuming the processedsignals as Y and that there is

Y = BX, (2)

where B is the (𝑀− 1) ×𝑀 preprocess blocking matrix,𝑀 isthe number of array elements, and B is given as

B =

[[[[[[[[[[

[

1 −𝑒−𝑗𝑢1 0 ⋅ ⋅ ⋅ 0 0

0 1 −𝑒−𝑗𝑢1 ⋅ ⋅ ⋅ 0 0

.

.

....

.

.

....

.

.

....

0 0 ⋅ ⋅ ⋅ 1 −𝑒−𝑗𝑢1 0

0 0 ⋅ ⋅ ⋅ 0 1 −𝑒−𝑗𝑢1

]]]]]]]]]]

]

. (3)

In the above formula, 𝑢1

= 2𝜋(𝑑/𝜆1) sin 𝜃

1, 𝜃1is the

azimuth of mainlobe interference, 𝜆1is the wavelength of the

narrowband interference, and 𝑑 is the spacing between twoadjacent array elements. Actually, B is the blocking matrixwhich is used to suppress the mainlobe interference based onthe adjacent antenna cancellation. Obviously, Y is the 𝑀 − 1

vector. Supposing the array antenna is the uniform lineararray with the element spacing 𝑑, the received signal of the𝑘th antenna before preprocess can be expressed as

𝑥𝑘 (𝑡) =

𝑃

∑

𝑖=0

𝑠𝑖 (𝑡) 𝑒𝑗(𝑘−1)𝑢

𝑖 + 𝑛𝑘 (𝑡) , (4)

where 𝑘 = 1, 2, . . . ,𝑀; 𝑢𝑖= 2𝜋(𝑑/𝜆

𝑖) sin 𝜃

𝑖stands for the

phase difference of the 𝑖th signal or interference arriving atthe array element between the two adjacent antenna; here, if𝑖 = 0, index 𝑖 stands for signal; if 𝑖 = 1, 2, . . . , 𝑃, it stands forinterference, but 𝑠

𝑖(𝑡) stands for the complex envelope of the

𝑖th signal or interference; 𝑛𝑘(𝑡) stands for the received noise

at the 𝑘th array element. After the processing with blockingmatrix preprocess, we can obtain the preprocessed signal

𝑦𝑘 (𝑡) =

𝑃

∑

𝑖=0

𝑠𝑖 (𝑡) 𝑒𝑗(𝑘−1)𝑢

𝑖 + 𝑛𝑘 (𝑡) , (5)

where 𝑘 = 0, 1, . . . ,𝑀 − 1, 𝑠𝑖(𝑡) = 𝑠

𝑖(𝑡)[1 − 𝑒

𝑗(𝑢𝑖−𝑢1)], and

𝑛𝑘(𝑡) = 𝑛

𝑘(𝑡)−𝑛

𝑘+1(𝑡). Comparing (4) and (5), the preprocess

transformation changes the complex envelope of signal,but does not change the corresponding DOA; meanwhilethe complex envelope 𝑠

𝑖(𝑡) equals zero for the mainlobe

interference. Therefore the blocking matrix preprocess cansuppress the mainlobe interference effectively and does notaffect desired signal and the other interference. For the otherinterference suppressing inside the sidelobe with nulling,the later adaptive beamforming can be implemented. At thesame time, the preprocess transformation will lose a freedomdegree of the array antenna.

In [6], the preprocess transformation is first used to pro-cess the received signal, and then the adaptive beamformingis used conventionally. The array covariance matrix aftertransformation is

R𝑌= 𝐸 [YY𝐻] = BAR

𝑆A𝐻B𝐻 + 𝜎

2

𝑛BB𝐻, (6)

where A is the steering vector matrix, R𝑆is the signal

covariance matrix, and 𝜎2

𝑛is the array noise covariance. At

last, using the classical optimal weight vector algorithm, theweight vector of the adaptive beamforming is given as

wopt = 𝜇R−1𝑌a𝑞, (7)

where 𝜇 is a constant and a𝑞is the steering vector of the

desired signal. Literature [6] mentioned that if the adaptivebeamforming is implemented by the above formula directly,it will lead to the problems of the sidelobe level rising andmainlobe shifting which is caused by mainlobe interferencesuppression; since the mainlobe shifting is caused by thepreprocess transformation matrix B, so [6] puts forwardthe weight coefficient compensation for the adaptive weightvector which is given as follows:

wopt = 𝜇R−1𝑌

(BB𝐻) a𝑞. (8)

Obviously, the nature of the weight vector compensationis that the original steering vector a

𝑞is multiplied by BB𝐻;

that is to say, (BB𝐻)a𝑞substitutes for the steering vector a

𝑞.

Next, we will analyze the reason why the mainlobe willshift after interference suppression with blocking matrixpreprocess in theory and give the efficient solution.

3. Improved Mainlobe InterferenceSuppression Method

3.1. Mismatch Analysis for BlockingMatrix Preprocess Method.Through the above analysis of the realization of the main-lobe interference suppression based on the blocking matrixpreprocess which is proposed in [6], we can know that whenthe received array data is multiplied by the blocking matrix,according to formula (5), the preprocess can suppress themainlobe interference effectively, but the complex envelopesof the desired signal and other interference are changed, buttheir DOAs do not change. We can do the following analysisfor the proposed idea with the array model after the blockingmatrix preprocess.

Journal of Electrical and Computer Engineering 3

Take the full representation for formula (5); there is

𝑦𝑘 (𝑡) =

𝑃

∑

𝑖=0

𝑠𝑖 (𝑡) [1 − 𝑒

𝑗(𝑢𝑖−𝑢1)] 𝑒𝑗(𝑘−1)𝑢

𝑖 + 𝑛𝑘 (𝑡) . (9)

For the mainlobe interference, when 𝑖 = 1, since 1 −

𝑒𝑗(𝑢𝑖−𝑢1)= 0, so this interference need not be considered here

and it does not affect the description of the received arraydata with the above formula. The received array data of thedesired signal and other interference after the blockingmatrixpreprocess can be expressed as

Y1= A1S1+ n1. (10)

In the above formula, S1stands for the received signal

which consists of the remaining sidelobe interference anddesired signal vectors, except the removed mainlobe inter-ference, but their complex envelopes have been changed as𝑠𝑖(𝑡)[1 − 𝑒

𝑗(𝑢𝑖−𝑢1)]; A1stands for the steering matrix of the

desired signal and remaining interferences correspondingly,n1is the received array noise after transformation, Y

1is the

received array data after blocking matrix preprocess, andactually Y

1is the same with the above Y; in order to simplify

the analysis, the symbols are uniformed and we have

Y1= Y. (11)

The DOA of desired signal does not change after prepro-cess, but the process loses a freedom degree of array antenna;the steering vector of the desired signal and remaininginterference with preprocess lose one dimension relative tothe unpreprocessed steering vector; the other parameter ofthe steering vector does not change. Assuming the receivedspace signals only consist of the desired signal and remaininginterferences and, now, the adaptive array processing isimplemented by the front 𝑀 − 1 antennas for the receivedarray data, then the received array signal of the correspondingarray can be expressed as

Y0= A0S0+ n0. (12)

Obviously, there are

A1= A0,

S1= S0Λ,

(13)

where

Λ = diag {1 − 𝑒𝑗(𝑢0−𝑢1), 1 − 𝑒

𝑗(𝑢2−𝑢1), . . . , 1 − 𝑒

𝑗(𝑢𝑃−𝑢1)} . (14)

So we have

R𝑌= 𝐸 [YY𝐻] = 𝐸 [Y

1Y𝐻1] = A

1R𝑆1A𝐻1+ 𝐸 [n

1n𝐻1]

= A0R𝑆1A𝐻0+ 𝜎2

𝑛BB𝐻,

(15)

where

R𝑆1

= 𝐸 [S1S𝐻1] = 𝐸 [S

0ΛΛ

HS𝐻0] . (16)

Similarly, there is

R𝑌0

= 𝐸 [Y0Y𝐻0] = A

0R𝑆0A𝐻0+ 𝐸 [n

0n𝐻0]

= A0R𝑆0A𝐻0+ 𝜎2

𝑛I,

(17)

where I is the identity matrix and

R𝑆0

= 𝐸 [S0S𝐻0] . (18)

Comparing the expressions of R𝑌and R

𝑌0, we can know

that both have certain differences whether between thecovariancematrix items of the desired signal and interferenceor between the covariance matrix items of the noise. In theadaptive beamforming, for R

𝑌and R

𝑌0, the same steering

vectors are used, but the array covariancematrixes are not thesame, so the difference of array processing results will existand be obvious.

Comparing the weight vector that is solved with the idealcovariance matrix R

𝑌0with that in [6] which is solved by

formula (7), we can see that the adaptive beamforming pro-cess has the covariance matrix mismatch or error. Thereforeit leads to the results that the mainlobe deviates from thedesired signal direction. And from the above analysis, themethod of weight coefficient compensation that is proposedin [6] is also difficult to obtain the desired effect.

In order to overcome the mentioned problem thatexists in the proposed method in [6], this paper proposesthe improved method which uses the diagonal loading toovercome the problem of the mainlobe direction shifting.Since the diagonal loading leads to the interference nullingdeclining, then the linear constraints are put forward toimprove the performance of other interferences suppression.

3.2. Improving Beam Pointing with Diagonal Loading. Diag-onal loading is a common beamforming technology; forsome undetermined problems, such as when the samplenumber is less than array processing freedom, the samplecovariance matrix will be not inversion, but diagonal loadingcan solve the beamforming problem [12–14]. We all knowthat the diagonal loading can increase the robustness ofthe beamformer; since diagonal loading can provide therobustness against the mismatch of the signal DOAs or arrayelement location and the gain or phase disturbances, it canalso restrain the covariancematrixmismatch that is caused bylimited samples supporting or covariance matrix estimationerror. Diagonal loading also can be used as a reducingdimension technology; it can shield off the influence aboutthe eigenvector that corresponds to the small eigenvalue andthen reduces the adaptive freedom degree.

Diagonal loading is realized by making the covariancematrix added with a diagonal matrixand often is formulatedas follows:

R̃𝑌= R𝑌+ 𝜎2

𝐿I, (19)

where𝜎2𝐿is used to control the amount of loading and is called

the loading level.


The core and key of the diagonal loading is to select theloading level; of course the ultimate choice of loading levelis determined by the adaptive beamforming algorithm orspecial application. If the loading level is smaller, loadingeffect is similar to unloading. On the contrary, if the loadinglevel is higher, the effect is similar to no adaptiveness (therank is 1), and the loading process shields off all the adaptivefreedom. In the adaptive array signal processing, the optimalloading level is generally selected to be higher than theaverage power 𝜎2

𝑛of the background noise but lower than the

power of the signal and interference.The experiencedmethodin the signal processing is to select the loading level whichis 5∼10 dB higher than the power of the background noise[13]. For some robust beamformer with norm or uncertaintyset constraint, the diagonal loading can be determined by theconstraint parameter [14, 15].

Since the purpose of diagonal loading is to improvethe mainlobe pointing, when the loading is very small,its improvement is not obvious; when the loading is verylarge, although the mainlobe can accurately point the desireddirection, the interference nulling steering does not aim at theactual interference direction.These factorsmake the choice ofloading level more difficult; from the simulation, this papersuggests that the loading level should be selected to be aslarge as possible; it will first ensure the accurate pointingto the desired direction and then improve the interferencenulling performance by additional linear constraints. It notonly meets the desired requirement for the array pattern,but also makes the choice of the loading level easier; whenthe selected loading level is very large, the choice and itsvalue will be not sensitive to the beamforming algorithm.Therefore, in order to obtain the desired performance of thebeam pointing, the corresponding loading level should beselected as a larger number.

3.3. Improving Other Interference Suppression with LinearConstraints. In order to obtain a desired direction signaland make other signals and noise output minimum, wecan select the linear constrained minimum power (LCMP)beamformer. The weight vector of LCMP beamformer canbe solved by making the output power minimum when thebeamformer is under a series of linear constraints such asC𝐻w = f , where C is the 𝑃 × (𝑀− 1) constraint matrix and fis the 𝑃 × 1 constraint vector [16, 17].

The optimization problem of LCMP beamformer can bedescribed as

minw w𝐻R𝑌w

s.t. C𝐻w = f .(20)

The optimization problem can be solved by Lagrangemultiplier method. The optimal weight vector can beexpressed as [17]

w = R−1𝑌C (C𝐻R−1

𝑌C)−1

f . (21)

When the diagonal loading technology is used, thecorresponding weight vector can be expressed as

w̃ = R̃−1𝑌C (C𝐻R̃−1

𝑌C)−1

f

= (R𝑌+ 𝜎2

𝐿I)−1

C [C𝐻 (R𝑌+ 𝜎2

𝐿I)−1

C]

−1

f .(22)

Therefore, when taking the adaptive LCMP beamformingafter array data preprocess, while the diagonal loading tech-nique is also used, we can make the mainlobe point at thedesired direction and form the deep nulling steering at theinterference direction. In particular, themethods proposed inthis paper not only have the better performance of mainlobeinterference suppression, but also make the choice of thediagonal loading level very easy and simple.

4. Simulation Analysis

In order to validate the effectiveness of the proposedmethod,the simulation analysis is given as follows. By the DOAestimation and beamformingwith the received array data andthe preprocessed array data, the performance of themainlobeinterference suppression is verified. Through the beamform-ingwith different processingmethods, the effectiveness of theproposed method is analyzed.

Assuming the antenna is the uniform linear array, thenumber of array elements is 𝑁 = 8, array element spacingis half of the signal wavelength, array sampling number 𝐾 =

1024, signal azimuth 𝜃0

= 0∘, there are three interferences

and their azimuths are 𝜃𝑖= [5, −30, 40]∘, signal to noise

ratio SNR = 10 dB, and interference to noise ratio is INR =[10, 10, 10] dB. Since the mainlobe width is about 20∘, theinterference with 𝜃

𝑖= 5∘ is inside the mainlobe.

4.1. Effectiveness Analysis. First, the MUSIC spatial spectrumestimation is used to verify the effectiveness of the mainlobeinterference suppression. Then the different beamformingalgorithms are taken for the original array data and thepreprocess array data, and the performance of the spatialfiltering for each algorithm is analyzed.

Figure 1 gives the results of MUSIC spatial spectrumestimation, wherein “MUSIC” stands for the result ofMUSICbefore preprocess, and “preprocess MUSIC” represents theresult of MUSIC after preprocess. Obviously the blockingmatrix preprocess eliminates themainlobe interference effec-tively, and the preprocess array data can be used for later arrayprocessing, such as adaptive beamforming for desired signal.

Figure 2 shows the compared results of the adaptivebeamforming pattern, “Capon” [18] and “preprocess” [6]stand for the Capon pattern before and after preprocess,“PP compensation” [6] represents the array pattern after pre-process and with weight vector compensation, “PP diagonalloading” [12] denotes the array pattern after preprocess andwith diagonal loading, and “PP DL and linear constraint”stands for the array pattern after preprocess and with diag-onal loading and linear constraints. Namely, the “Capon”beamforming uses the original array data, the other beam-forming uses the array data with blocking matrix preprocess.


0 50 100

0

10

20

30

40

50

60

Azimuth angle (deg)

MU

SIC

spec

trum

(dB)

MUSICPreprocess MUSIC

−100 −50

−10

Figure 1: MUSIC spatial spectrum estimation (1).

0 50 100

0

Azimuth angle (deg)

Beam

form

er p

atte

rn (d

B)

CaponPreprocess (PP)PP compensation

PP diagonal loadingPP DL and linear constraint

−45

−40

−35

−30

−25

−20

−15

−10

−5

−100 −50

Figure 2: Adaptive beamforming pattern (1).

The pattern parameters, such as mainlobe direction, main-lobe width, maximum sidelobe level, and nulling depth,are given in Figure 3, wherein the abscissa is the index ofthe five processing methods; the index from 1 to 5 denotesthe “Capon,” “preprocess,” “PP compensation,” “PP diagonalloading,” and “PP DL and linear constraint,” respectively.

From the beamforming patterns in Figure 2 and com-paring the pattern parameters in Figure 3, we can see thatdue to the interference in mainlobe the array pattern of theconventional Capon will form a deep null steering and thenlead to a serious mainlobe deformation with peak shifting.The Capon pattern based on preprocess array data restrainsthe mainlobe interference, but the mainlobe has certainshifting; the result of weighted vector compensation is verypoor. The diagonal loading after preprocess can overcome

1 1.5 2 2.5 3 3.5 4 4.5 50

10

20

30

Method index

ML

para

met

er (d

eg)

Beam directionMainlobe width

(a) Mainlobe direction and width

1 1.5 2 2.5 3 3.5 4 4.5 5Method index

SL p

aram

eter

(dB)

Maximum sidelobeNulling depth

−40

−30

−20

−10

(b) Maximum sidelobe level and nulling depth

Figure 3: Mainlobe and sidelobe parameters (1).

MUSICPreprocess MUSIC

0 50 100

0

10

20

30

40

50

60

Azimuth angle (deg)

MU

SIC

spec

trum

(dB)

−100 −50

−10

Figure 4: MUSIC spatial spectrum estimation (2).

the mainlobe shifting effectively, but the interference nullingis poor. The proposed method with combining the diagonalloading and linear constraints after preprocess not onlyrealizes the mainlobe interference suppression, but also hasthe accurate desired pointing and interference nulling.

To further verify the correctness of the proposed algo-rithm, array configuration is same as former, but theazimuths of signal and interference are 𝜃

0= −10

∘ and 𝜃𝑖

= [−5, −40, 30]∘, respectively. The corresponding results ofspatial spectrum estimation and adaptive pattern are shownin Figures 4, 5, and 6. Here, the proposed method alsoachieves the desired performance of the adaptive processing.


0

Beam

form

er p

atte

rn (d

B)

−40

−50

−30

−20

−10

CaponPreprocess (PP)PP compensation

PP diagonal loadingPP DL and linear constraint

0 50 100Azimuth angle (deg)

−100 −50

Figure 5: Adaptive beamforming pattern (2).

1 1.5 2 2.5 3 3.5 4 4.5 5

0102030

Method index

ML

para

met

er (d

eg)

−10



1 1.5 2 2.5 3 3.5 4 4.5 5Method index

SL p

aram

eter

(dB)

−40

−30

−20

−10



Figure 6: Mainlobe and sidelobe parameters (2).

Therefore, from the above comparison and analysis, wecan deduce that the proposedmethod is correct and effective.

4.2. Diagonal Loading Analysis. In this paper, the causeof mainlobe shifting is analyzed, which is because thecovariance matrix mismatch exists in adaptive beamforming.Therefore, the diagonal loading is proposed to overcome thismismatch, but how to select the loading level is the keyproblem in its realization. Hence, the diagonal loading level

0

Beam

form

er p

atte

rn (d

B)

−40

−50

−60

−30

−20

−10

0 50 100Azimuth angle (deg)

−100 −50

Minimize DLMaximize DL

Capon DL (min to max)

Figure 7: Capon pattern with diagonal loading.

0 50 100

0

Azimuth angle (deg)

Beam

form

er p

atte

rn (d

B)

−45

−40

−35

−30

−25

−20

−15

−10

−5

−100 −50

Minimize DLMaximize DL

LCMP DL (min to max)

Figure 8: LCMP pattern with diagonal loading.

affects the performances of the traditional beamforming andthe proposed method is analyzed in detail.

Figures 7 and 8 show the effects of the loading level on thebeam pattern of the Capon beamforming algorithm and theLCMP beamforming algorithm after blockingmatrix prepro-cess, respectively. Figures 9 and 10 show the pattern param-eters of the mainlobe and sidelobe for Capon and LCMPbeamformer with diagonal loading, respectively. Figures 11and 12 show the output SNR curves of the correspondingadaptive beamformers, respectively.

In Figures 7 and 8, “minimize DL” and “maximizeDL” stand for the patterns when the loading level takesthe minimum and maximum value, respectively, whereinthe minimum and maximum loading level are selected aszero and ten times the largest eigenvalue of the samplecovariancematrix. “CaponDL (min tomax)” and “LCMPDL


0 1 2 3 40

10

20

30

DL factor

ML

para

met

er (d

eg)

×104



0 1 2 3 4DL factor

SL p

aram

eter

(dB)

−30

−20

−10


×104


Figure 9: Mainlobe and sidelobe parameters of Capon beamformerwith diagonal loading.

0 1 2 3 40

10

20

30

DL factor

ML

para

met

er (d

eg)

×104



0 1 2 3 4DL factor

SL p

aram

eter

(dB)

−30

−40

−20

−10

×104



Figure 10:Mainlobe and sidelobe parameters of LCMPbeamformerwith diagonal loading.

(min to max)” represent the patterns when the Capon andLCMP beamforming algorithm with the loading level takethe numerical value between the minimum and maximumvalues, respectively.

By comparing the array patterns of the Capon and LCMPbeamformers in Figures 7 and 8 and comparing their pattern

0 1 2 3 4 50.4

0.5

0.6

0.7

0.8

0.9

DL factor

Out

put S

NR

(dB)

×104

Capon with DLPreprocess (PP)

Max diagonal loadingDL and linear constraint

Figure 11: Output SNR of Capon beamformer with diagonalloading.

0 1 2 3 4 50.4

0.5

0.6

0.7

0.8

0.9

DL factor

Out

put S

NR

(dB)

×104

Capon with DLLCMP with DL

Figure 12: Output SNR of LCMP beamformer with diagonalloading.

parameters in Figures 9 and 10, when the loading level isselected as the minimum value, namely, zero, in fact, withoutdiagonal loading, their mainlobes are all shifting, but whenthe diagonal loading is used, the two beamformers havethe better mainlobe pointing performance. But the Caponbeamformer has poor ability to suppress the interferenceswhich are out of mainlobe.

In Figures 11 and 12, “Capon with DL” and “LCMPwith DL” stand for the corresponding output SNRs whenCapon and LCMP beamforming algorithm with diagonalloading take the numerical value between minimum andmaximum values. “Preprocess” denotes the output SNR ofCapon beamforming with blocking matrix preprocess; “maxdiagonal loading” represents the output SNR of the Capon


beamformer with the largest diagonal loading level andblockingmatrix preprocess. In Figure 11, the curve of “DL andlinear constraint” is the same as that of “LCMP with DL” inFigure 12.

From Figures 11 and 12, we can see that the selectionof the diagonal loading level has great effect on the Caponbeamforming after blocking matrix preprocess, but, withthe loading level increasing, the variation of the patternis not very obvious; meanwhile the output SNR of thebeamformer also tends to a constant. However, for the LCMPbeamforming after blocking matrix preprocess, the selectionof diagonal loading level has very little effect on pattern andthe corresponding output SNR. Therefore, for the proposedmethod in this paper, the selection of loading levelwill be veryeasy and simple.

5. Conclusion

For the problem of mainlobe direction shifting that is causedby the mainlobe interference suppression based on blockingmatrix preprocess, this paper finds that the covariancematrixerror exists in the array data after the blocking matrixpreprocess, which will lead to covariance matrix mismatchin the later adaptive beamforming, and then results in themainlobe shifting.Therefore, an effectivemethod is proposedto improve the performance of the mainlobe interferencesuppression which is based on the combination of diagonalloading and linear constraints, which meanwhile realizes theprecise pointing of the mainlobe and other interferencesnulling. Therein, the effect of diagonal loading level on thebeamforming algorithms is analyzed, and it deduces that theproposed method is not sensitive to the selection of diagonalloading level; in other words, its realization is simple andeffective.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

The authors would like to thank the anonymous reviewersfor their valuable comments. This work was supported inpart by the National Natural Science Foundation (61402365,61271300), the Shaanxi Education Natural Science Founda-tion (2013JK1076), theNational Visiting Scholarship Program(201406965022), and the Shaanxi Industry Surmount Foun-dation (2013K-33, 2014KW01-04).

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